Related papers: A note ON MONOGENEITY of pure number fields
In this paper, we introduce the notion of unit reducibility for number fields, that is, number fields in which all positive unary forms attain their nonzero minimum at a unit. Furthermore, we investigate the link between unit reducibility…
This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…
This paper also has excessove overlap with the following papers also written by the authors or their collaborators: gr-qc/0502060, gr-qc/0606028, gr-qc/0511095, gr-qc/0505078, gr-qc/0603044, gr-qc/0608014, gr-qc/0510123, gr-qc/0607109,…
In this article, we explore the structure of IR singularity of Feynman diagrams at one loop via power counting in loop momentum. The emphasis is on many known results which follow from this simple analysis.
In this paper, the conditions of monogenicity are weakened for functions with values in a three-dimensional commutative algebra over the field of complex numbers. By monogenicity we mean continuity and the existence of the G\^ateaux…
Let $K = \mathbb{Q} (\alpha) $ be a pure number field generated by a complex root $\alpha$ of a monic irreducible polynomial $ F(x) = x^{2^u\cdot 3^v}-m$, with $m \neq \pm 1$ a square free rational integer, $u$, and $v$ two positive…
This work studies the complexity of refuting the existence of a perfect matching in spectral expanders with an odd number of vertices, in the Polynomial Calculus (PC) and Sum of Squares (SoS) proof system. Austrin and Risse [SODA, 2021]…
We correct some tables and figures in [A.P. Bustamante and R.C. Calleja, Physica D: Nonlinear Phenomena, 395 (2019), pp. 15-23, arXiv:1712.05476]. We also report on the new computations that verify the accuracy of the data and extend the…
In this paper, the author introduces hyperfields and give some facts about the roots and multiplicities of polynomials over hyperfield based on \cite{2} and \cite{3}. Then he tests the sharpness of an inequality in Baker's former work…
Recently (Science, 355, 6320, 2017, 49-52) it was argued that density functionals stray from the path towards exactness due to errors in densities (\rho) of 14 atoms and ions computed with several recent functionals. However, this…
We give some properties of skew spectrum of a graph, especially, we answer negatively a problem concerning the skew characteristic polynomial and matching polynomial in [M. Cavers et al., Skew-adjacency matrices of graphs, Linear Algebra…
This is a short note that explains a problem on polynomial maps over finite fields for non-experts. The problem is: Do there exist odd polynomial automorphisms over the finite fields with 4,8,16,32,64,... elements? The explanation is very,…
Consider a polynomial $f$ defined over a field $k$, the multiplicity is perhaps the most naive measurement of the singularities of $f$. This paper describes the first steps toward understanding a much more subtle measure of singularities…
The generalization of the Morse theory presented by Goresky and MacPherson is a landmark that divided completely the topological and geo\-me\-tri\-cal study of singular spaces. Let \{$X_t\}_t$ be a suitable family of germs at $0$ of…
Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…
This note will study complex polynomial maps of degree $n\ge 2$ with only one critical point.
In this note we make a minor correction to the paper ``Simplicial monoids and Segal categories."
We compute the expected value of various quantities related to the biparametric singularities of a pair of smooth centered Gaussian random fields on an n-dimensional compact manifold, such as the lengths of the critical curves and contours…
The theory of isomorphs is reformulated by defining Roskilde-simple systems (those with isomorphs) by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a…